The distance and direction of the ship from the starting point is found using vectors as follows;
The ship is 48.03 nautical miles from the starting point at a directional bearing of N 18.53° E
What are vectors?A vector is a quantity that has a property of magnitude or size and direction.
The ship's speed = 36 nautical miles per hour
Direction of the ship = Due east
The duration the ship continues in the direction = 1 hour
The new direction of the ship = N32°E
The duration in which the ship continues in the new direction = Half an hour
The vector of the distances traveled by the ship are;
[tex]\overrightarrow{d_1}[/tex] = 36·i
[tex]\overrightarrow{d_2}[/tex] = 0.5 × 36×sin(32°)·i + 0.5 × 36×cos(32°)·j = 18×sin(32°)·i + 18×cos(32°)·j
The sum of the distances traveled by the ship is therefore;
36·i + 18×sin(32°)·i + 18×cos(32°)·j = (36 + 18×sin(32°))·i + 18×cos(32°)·j
(36 + 18×sin(32°))·i + 18×cos(32°)·j = 45.54·i + 15.26·j
The distance of the ship from the starting point, d, is therefore;
d ≈ √(45.54² + 15.26²) ≈ 48.03
The distance of the ship from the starting point is approximately 48.03 miles.
The direction from the North of the ship from its starting point, θ, is therefore;
[tex]\theta = arctan\left(\dfrac{15.26}{45.54} \right) \approx 18.53^{\circ}[/tex]
Then direction of the ship is N 18.53° E
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The time is takes an object to move a certain distance is inversely propotional to the speed that it's travelling at.
it takes a car 12 minutes to travel the length of a road if it goes at an average speed of 60mph
a) How long would it take the car to travel down the same road if it travelled at an average speed of 30mph
Answer:
Hope the picture will help you
Find the intercepts of the line
Answer:
x-int=-40
y-int=15
Step-by-step explanation:
we have points 0,15 and -40,0 on the line.
It is as easy as the y-int being 15 and the x-int being -40!
the y-int will always be= (0,#)
the x-int will always be (#,0)
Mia tasted ocean water and found it very salty which statement best explains the salty nature of ocean water?
I think the answer is C. Because the energy from the sun does break Down rocks and release salt
A house was valued at $321,000. Over several years, the value decreased by 9%, giving the house a new value.
Answer:
The new value is $292,110
Step-by-step explanation:
321,000 - (1 - 0.09) = 292,110
Calculate the simple interest and maturity value
The simple interest is $420 and the maturity value is $$6,720
How to find the simple interest?Using this formula to find the simple interest
Simple interest = Principal × Interest rate × Time
Where:
Principal = $6300
Interest rate =4% or 0.04
Time = 20 month = 20/12 = 1.6666666
Let plug in the formula
Simple interest = $6,300 × 0.04 × 1.6666666
Simple interest = $420
Using this formula to find the maturity value
Maturity value = Principal + Interest
Maturity value = $6,300 + $420
Maturity value = $6,720
Therefore the interest is $420.
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Write an exponential function represented by the graph
y= ?
Answer:
y = 8 [tex](\frac{1}{2}) ^{x}[/tex]
Step-by-step explanation:
an exponential function can be expressed in the form
y = a [tex]b^{x}[/tex]
to find a and b use points that lie on the graph
using (0, 8 ) , then
8 = a[tex]b^{0}[/tex] [ [tex]b^{0}[/tex] = 1 ] , then a = 8
y = 8[tex]b^{x}[/tex]
using (1, 4 ) , then
4 = 8[tex]b^{1}[/tex] = 8b ( divide both sides by 8 )
[tex]\frac{4}{8}[/tex] = b , that is b = [tex]\frac{1}{2}[/tex]
y = 8 [tex](\frac{1}{2}) ^{x}[/tex] is the exponential function
What miles per gallon did the car get after 280 miles using 8 gallons of gas?
Answer: 35 miles
Step-by-step explanation:
First we divide 280 by 8 to get the answer per gallon. 280 / 8 = 35, therefore each gallon equals 35 miles.
find the 73rd term of the following arithmetic sequence 18,22,26,30
The arithmetic sequence has the 73rd term of 306
How to find the 73rd term for the arithmetic sequence?The sequence is given as:
18,22,26,30,....
The above sequence has the following parameters
First term, a = 18Common difference, d = 4 i.e. 22 - 18 = 4Number of terms , n = 73This means that the sequence is an arithmetic sequence
The nth term of an arithmetic sequence is calculated as
f(n) = a + (n - 1) * d
Substitute the known values in the above equation
So, we have the following equation
f(73) = 18 + (73 - 1) * 4
Evaluate
f(73) = 306
Hence, the 73rd term for the arithmetic sequence is 306
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What is the expected change in the dividend of a 6% preferred stock if the required rate of return drops instantly from 8% to 6%?
The expected change in the dividend of a 6% preferred stock is $75.
Given that, the required rate of return drops instantly from 8% to 6%.
What is the return?A return, also known as a financial return, in its simplest terms, is the money made or lost on an investment over some period of time.
The value of preferred stock = $100
Annual dividend = 100 × 6% = $6
Price of preferred stock when required return is 8% = Annual dividend / Required rate of return
= 6/8%
= 6 ×100/8
= $75
Therefore, the expected change in the dividend of a 6% preferred stock is $75.
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a notebook manufacturer expectations fixed monthly costs of $46and variables costs of $1.50 per notebook produced.The notebooks are then sold for $3.50.
Answer: 13
Step-by-step explanation:
Add.
−1 4/5 + (−1/4) + (−1/5)
The required simplified value of the given expression is given as -13/20.
Given that,
An expression is given, −1 4/5 + (−1/4) + (−1/5) we have to determine the sum of the expression.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
here,
= -1 4/5 + (-1/4) + (-1/5)
= -1/5 -1/4 -1/5
= -2/5 -1/4
= -13/20
Thus, the required simplified value of the given expression is given as -13/20.
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14 11/12 + 3 1/6 need help
Answer:
18.0833333333
Step-by-step explanation:
online calculator
Quincy has a jewelry business in which he designs and sells bracelets. His daily profit, Q(x), can be modeled by the function Q(x) = 8.25x − 24.75, where x is the number of bracelets he sells. What is the value of Q(3), and what is its interpretation?
Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.
Q(3) = 0; If Quincy sells 0 bracelets, he will earn $3.
Q(3) = 3.36; If Quincy sells 3 bracelets, he will earn $3.36.
Q(3) = 3.36; If Quincy sells 3.36 bracelets, he will earn $3.
The correct interpretation is Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Q(x) = 8.25x − 24.75, where x is the number of bracelets he sells.
So, for x= 3 them Q(3)
Q(3)= 8.25 (3) - 24.75
Q(3) = 24.75 - 24.75
Q(3) = 0
Hence, Q(3) = 0; If Quincy sells 3 bracelets, he will earn $0.
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I don’t know it and I need help. question is in picture
Mexico City had an estimated population of 18,066,000 people while Tokyo had an estimated population of 34,450,000 people. What was their combined population?
Answer:
Scientific notation: 5.2516 x [tex]10^{7}[/tex]
Standard notation 52,516,000
Step-by-step explanation:
Are you asking for the answer to be in scientific notation?
5.2516 x [tex]10^{7}[/tex] or 52,516,000
(1.8066 x [tex]10^{7}[/tex]) + (3.445 x [tex]10^{7}[/tex])
(1.8066 + 3.445) x [tex]10^{7}[/tex]
5.2516 x [tex]10^{7}[/tex]
System of Equations Question:
John is in charge of feeding the pigs and cows on the farm. The cow's food costs twice as much as the pig's food. There are 46 cows and 22 pigs on the farm. John has an $860 budget for food a month. How much can John spend on food for each cow per month?
The amount John will spend on food for each cow per month is approximately 15.08 dollars
How to find the how much each cow feed per month?John is in charge of feeding the pigs and cows on the farm.
The cow's food costs twice as much as the pig's food.
Let
x = cost of pigs food
y = cost cow's food
Hence,
y = 2x
There are 46 cows and 22 pigs on the farm. John has an $860 budget for food a month.
46y + 22x = 860
Therefore, let's combine the system of equation.
y = 2x
46y + 22x = 860
46(2x) + 22x = 860
92x + 22x = 860
114x = 860
x = 860 / 114
x = 7.5 dollars
y = 2(7.54) = 15.08 dollars
Therefore, the cost of food for each cow is 15.08 dollars
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A math class has a total of 33 students. The number of males is 15 more than the number of females. How many males and how many females are in the class?
(b) A local store is keeping track of service times. The table below
shows the number of customers served and the time it took.
Number of customers 2-6-7
Time (in minutes) 8-24-28
_It does not always take the same amount of time to serve each customer.
_It appears to take the same amount of time to serve each customer
Histogram for the following intervals will be,
5-9 (4)
10-14 (3)
15-19 (5)
20-24 (3)
What are histograms?The data are numerical.When establishing whether the output of a process is distributed roughly regularly, you want to see how the data are dispersed.determining whether a method can satisfy the needs of the customerexamining the appearance of the product of a supplier's procedureDetermining whether the outputs of two or more processes are different and determining whether a process has changed from one time period to another.You want to let others know about the rapid and simple sharing of data.Acc to our question-
On your y-axis, you would draw a frequency that goes up to 5. Because the data is sequential, make sure the bars are touching (in order).Name the customers on your x-axis.Label the frequency y-axis.hence, histogram will show the values.
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What is the value of csc 47° to the nearest thousandth?
Answer: 1.367
Step-by-step explanation:
csc47° = 1.3673 ≈ 1.367
The value of cosec 47° is 1.367.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
cosec 47°
The value of cosec 47°.
= 1.367334
Rounding to the nearest thousandth.
= 1.367
Thus,
The value of cosec 47° is 1.367.
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Evaluate y(x ÷ 2) if x is 20 and y is 10
Answer:
100
Step-by-step explanation:
x = 20
x ÷ 2
= 20 ÷ 2
= 10
y = 10
y ( x ÷ 2 )
= 10 x 10
= 100
Determine the slope-intercept form of the equation of the line parallel to y = -4/3x + 11 that passes through the point (–6, 2). y = x +
The equation of the line in slope-intercept form is y = -4x/3-6 when the line is parallel to y = -4x/3+11.
According to the question,
We have the following information:
The line is parallel to y = -4/3x + 11 and passes through the point (–6, 2).
Now, we know that the following formula is used to find the equation of the line:
y-y' = m(x-x')
In this case, m is the slope of the line.
m = -4/3
We have the following values:
x' = -6 and y' = 2
Now, we have the following expression:
(y-2) = -4/3(x+6)
y-2 = -4x/3-8
Adding 2 to both sides of the equation:
y = -4x/3-8+2
y = -4x/3-6
Hence, the equation of the line in slope-intercept form is y = -4x/3-6 when the line is parallel to y = -4x/3+11.
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Find the volume of the rectangular prism.
8 m
8 m
8 m
Answer:
Step-by-step explanation:
I believe that the volume of the rectangular prism is 512.
Explanation: V = whl = 8 · 8 · 8 = 512
V=Volume
W= Width
H= Height
L= Length
The animals at a safari park include camels,
kangaroos and meerkats.
There are 12 more kangaroos than there are
camels.
There are 3 times as many meerkats as there
are camels.
There are the same number of kangaroos as
there are meerkats.
How many camels are there at the safari park?
Describe the features of the function that can be easily seen when a quadratic function is given
in the form: y= A(x−A )( x− B) and how they can be identified from the equation.
The features of the functions when a quadratic function is given in the form: y = a (x − p) (x − q)
y = value in the y coordinates
a = constant in the equation
p and q = zeros or roots
x = value in the x coordinates
How to identify features in the equationWhen quadratic equation is written of the form y = a (x − p) (x − q), it is called the factored form of quadratic equation
The other form is ax^2 + bx + c and called standard form of quadratic equation
a in both cases are same and it helps to da if the curve opens upward or downward
when a is positive the curve opens upward but when it is negative the curve opens downward
Expanding the factored form of quadratic equation brings the equation to the standard form
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find the volume, of the box that is 3ft, 4ft, 6ft
2.) lee has seven 5-dollar bills and le quarters
in his pocket. How much money would he have
left in his pocket if he buyes a leather jacket
worth $35.20.
Amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.
As given in the question,
Conversion of quarter into dollars is :
1 quarter = 0.25 dollars
Amount of money with Lee in his pocket is equal to :
= ( 7 × 5) dollars + ( 6 × 0.25) dollars
= (35 +1.5) dollars
=$ 36.5
Cost of leather jacket buy by Lee = $35.20
Amount of money left in lee's pockets after purchasing jacket
= $( 36.5 - 35.20)
= $ 1.3
Therefore, amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.
The complete question is :
Lee has seven 5-dollar bills and 6 quarters in his pocket. How much money would he have left in his pocket if he buys a leather jacket
worth $35.20?
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Multiply the difference of 10 and 8 by 4 expression
The Mathematical Expression formed is 4(10-8)
What is a Mathematical Expression?
In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations.
Solution:
The mathematical expression formed frrom the statement;
Multiply the difference of 10 and 8 by 4
is as follows,
4(10-8)
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How do I solve the following equation?
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{3}}x+7\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is -1/3 and that it passes through (-2 , 5.5)
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{5.5})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5.5}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{(-2)}) \implies y -5.5= -\cfrac{1}{3} (x +2)[/tex]
[tex]y-5.5=-\cfrac{1}{3}x-\cfrac{2}{3}\implies y=-\cfrac{1}{3}x-\cfrac{2}{3}+5.5\implies y=-\cfrac{1}{3}x-\cfrac{2}{3}+\cfrac{55}{10} \\\\\\ y=-\cfrac{1}{3}x-\cfrac{2}{3}+\cfrac{11}{2}\implies {\Large \begin{array}{llll} y=-\cfrac{1}{3}x+\cfrac{29}{6} \end{array}}[/tex]
It is expected that 750 people will attend
the concert. In fact, 600 people attended.
600 is what percent of the expected
number?
600 is the 80% of the the expected number
Number of people that expected to attend the concert = 750 people
Number of people that attended the concert = 600 people
600 is what percent of the expected number = ( Number of people that attended the concert ÷ Number of people that expected to attend the concert ) × 100
Substitute the values in the equation
600 is what percent of the expected number = (600 / 750) × 100
Divide the terms in bracket first
= 0.8 × 100
Multiply the given terms
= 80%
Hence, 600 is the 80% of the the expected number
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